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Simplifying -16t2 + 33t + 5 = 0 Reorder the terms: 5 + 33t + -16t2 = 0 Solving 5 + 33t + -16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.3125 + -2.0625t + t2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + -2.0625t + 0.3125 + t2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + -2.0625t + t2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + -2.0625t + t2 = 0 + 0.3125 -2.0625t + t2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 -2.0625t + t2 = 0.3125 The t term is -2.0625t. Take half its coefficient (-1.03125). Square it (1.063476563) and add it to both sides. Add '1.063476563' to each side of the equation. -2.0625t + 1.063476563 + t2 = 0.3125 + 1.063476563 Reorder the terms: 1.063476563 + -2.0625t + t2 = 0.3125 + 1.063476563 Combine like terms: 0.3125 + 1.063476563 = 1.375976563 1.063476563 + -2.0625t + t2 = 1.375976563 Factor a perfect square on the left side: (t + -1.03125)(t + -1.03125) = 1.375976563 Calculate the square root of the right side: 1.173020274 Break this problem into two subproblems by setting (t + -1.03125) equal to 1.173020274 and -1.173020274.Subproblem 1
t + -1.03125 = 1.173020274 Simplifying t + -1.03125 = 1.173020274 Reorder the terms: -1.03125 + t = 1.173020274 Solving -1.03125 + t = 1.173020274 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.03125' to each side of the equation. -1.03125 + 1.03125 + t = 1.173020274 + 1.03125 Combine like terms: -1.03125 + 1.03125 = 0.00000 0.00000 + t = 1.173020274 + 1.03125 t = 1.173020274 + 1.03125 Combine like terms: 1.173020274 + 1.03125 = 2.204270274 t = 2.204270274 Simplifying t = 2.204270274Subproblem 2
t + -1.03125 = -1.173020274 Simplifying t + -1.03125 = -1.173020274 Reorder the terms: -1.03125 + t = -1.173020274 Solving -1.03125 + t = -1.173020274 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.03125' to each side of the equation. -1.03125 + 1.03125 + t = -1.173020274 + 1.03125 Combine like terms: -1.03125 + 1.03125 = 0.00000 0.00000 + t = -1.173020274 + 1.03125 t = -1.173020274 + 1.03125 Combine like terms: -1.173020274 + 1.03125 = -0.141770274 t = -0.141770274 Simplifying t = -0.141770274Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.204270274, -0.141770274}
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